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<title>Simulations for Statistical and Thermal Physics</title>
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<h3 style="text-align: center;">Java Simulations for Statistical and
Thermal Physics</h3>
<img src="disks.jpg" alt="" align="middle" border="1" height="277" width="300">
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<p>The following programs were written for the Statistical and Thermal
Physics curriculum development project and  are part of the <a href="http://www.opensourcephysics.org">Open Source Physics</a>
project. The programs are released under the <b>GNU
General Public License</b>.  The source code is <a href="http://stp.clarku.edu/simulations/source/stp_source.zip">available</a>.</p>

<p>You can run these programs as applets in a browser or <a href="http://stp.clarku.edu/simulations/osp_stp.jar">download</a> the Launcher as a stand-alone application (a jar file).</p>

<p>&nbsp;&nbsp;&nbsp;&nbsp;The goal of the simulations and calculations is to illustrate some
of the fundamental concepts in statistical mechanics. They can be used
as standalone programs, or in conjunction with a text such as Daniel
Schroeder, <a href="http://physics.weber.edu/thermal/"><i>An Introduction to Thermal Physics,</i></a> Addison-Wesley
(2000), or in conjunction with the online <a href="http://stp.clarku.edu/notes/">notes</a> by Harvey Gould and Jan
Tobochnik.</p>

<p>&nbsp;&nbsp;&nbsp;&nbsp;The programs were developed by Kipton Barros, Joshua Gould, Harvey
Gould, Natali Gulbahce, Peter Sibley, Jan Tobochnik, and most recently by Hui Wang and Ranjit Chacko.</p>

<ol>

<li><a href="approachtoequilibrium/index.html"><b>Approach to Equilibrium</b></a>. Explore some of the qualitative properties of macroscopic systems.</li>

<li><a href="demon/index.html"><b>An ideal thermometer</b></a>. Why is an extra degree of freedom called the demon an ideal thermometer?</li>

</ul>
</li>

<li><a href="sensitive/index.html"><b>Sensitivity to initial conditions</b></a>.
A molecular dynamics
simulation of a Lennard-Jones system in a specially prepared state.</li>

<li><a href="randomwalks/index.html"><b>Random walks</b></a>. What happens to a drunken sailor?</li>

<li><a href="cointoss/index.html"><b>Multiple coin toss</b></a>. Monte
Carlo simulation of the
statistical properties of the outcome of the tosses of many coins. </li>

<li><a href="binomial/index.html"><b>Binomial distribution</b></a>. The plots illustrate how the width and relative width depend on N, the number of steps. </li>

<li><a href="centrallimittheorem/index.html"><b>Central limit theorem</b></a>. A
demonstration of the probability
distribution of a random additive process.</li>

<li><a href="estimate/index.html"><b>Monte Carlo estimation</b></a>.
Estimation of the area under a curve
using the "hit or miss" method.</li>

<li><a href="multiplicativeprocess/index.html"><b>A simple multiplicative random
process</b></a>. The simulation illustrates the importance of rare events.</li>

<li><a href="boltzmann/index.html"><b>Boltzmann probability</b></a>. A
Monte Carlo simulation of an
ideal classical gas in one dimension in equilibrium with a heat bath.</li>

<li><a href="einsteinsolid/index.html"><b>Simple thermal interaction</b></a>.
Calculation of the number of states of two
harmonic solids that can exchange energy.</li>

<li><a href="einsteinsolidheatbath/index.html"><b>Einstein solid at temperature T</b></a>. Simulation of Einstein (harmonic) solid in equilibrium with a heat bath at temperature T using the Metropolis algorithm.</li>

<li><a href="entropy/index.html"><b>Entropy and temperature</b></a>. Calculation of the
entropy of two harmonic
solids that can exchange energy.</li>

<li><a href="thermalcontact/index.html"><b>Thermal equilibrium</b></a>. A
molecular dynamics simulation of
two solids in thermal contact. What quantity becomes the same in
thermal equilibrium?</li>

<li><a href="lj/index.html"><b>Lennard-Jones potential</b></a>. A <a href="lj/md/index.html">molecular dynamics</a> or <a href="lj/mc/index.html">Monte Carlo</a> simulation of a
liquid in two dimensions. Output includes the mean pressure,
temperature,  heat capacity, and the radial distribution function.</li>

<li><a href="harddisks/index.html"><b>Hard disks</b></a>. A <a href="harddisks/dynamics/index.html"> molecular
dynamics</a> or <a href="harddisks/metropolis/index.html">Monte Carlo</a> simulation of hard disks.
Output includes the mean pressure, the mean free path, and the mean collision time.</li>

<li><a href="ising/index.html"><b>Ising model</b></a>.

<ul>

<li><a href="ising/ising1d/index.html"><b>1D Ising model</b></a>. A Monte Carlo
simulation of the
one-dimensional Ising model. Output includes mean energy and heat
capacity.</li>

<li><a href="ising/ising2d/index.html"><b>2D Ising model</b></a>. A Monte Carlo
simulation of the
two-dimensional Ising model. Output includes the mean energy, heat
capacity, and the susceptibility.</li>

<li><a href="ising/antiferromagnet/index.html"><b>Simulation of the Ising antiferromagnet on a square lattice</b></a>.</li>

<li><a href="ising/triangularlattice/index.html"><b>Simulation of the Ising antiferromagnet on a triangular lattice</b></a>.</li>

<li><a href="ising/meanfield/index.html"><b>Mean-field solution</b></a>. Plot of the numerical solutions to the usual self-consistent equation and the corresponding free energy.</li>

<li><a href="ising/wanglandau/index.html"><b>Density of states of the 2D Ising
model</b></a>. A Monte Carlo
estimation of the density of states using the Wang-Landau algorithm.</li>

<li><a href="ising/partitionFunction/index.html"><b>Partition function of the 2D Ising model</b></a>. A Monte Carlo estimate of the partition function using a novel algorithm.</li>

</ul>
</li>

<li><a href="idealgas/index.html"><b>Ideal gas integrals</b></a>

<ul>
<li><a href="idealgas/bosegas.html"><b>Ideal Bose gas</b></a>. Calculation of
the chemical potential as a
function of temperature for fixed density for an ideal Bose gas.</li>

<li><a href="idealgas/fermigas.html"><b>Ideal Fermi gas</b></a>. Calculation
of the chemical potential as
a function of temperature for fixed density. The calculated chemical
potential is used to determine the mean energy.</li>
</ul>
</li>

<li><a href="numberofstates/index.html"><b>Number of states of a particle in a box</b></a>. A comparison of the actual number of states to the asymptotic expression.</li>

<li><a href="virial2/index.html">Second virial coefficient</a>.</li>

<li><a href="latticedemon/index.html"><b>Generalized demon algorithm</b></a>. A generalization of the demon algorithm that yields the chemical potential as well as the temperature.</li>

<li><a href="isinglatticegas/index.html"><b>Ising lattice gas</b></a>. A simulation of a lattice gas with different chemical potentials.</li>

<li><a href="widom/index.html"><b>Chemical potential</b></a>. An estimation of the chemical potential of a Lennard-Jones fluid using the Widom insertion method</li>

<li><a href="xymodel/index.html"><b>XY or planar model</b></a>. A
simulation of the two-dimensional XY
model. See the development of vortices below the Kosterlitz-Thouless
transition.</li>

<li><a href="fpu/index.html"><b>Fermi-Pasta-Ulam problem</b></a>.
Simulation of a chain of
oscillators coupled by anharmonic springs.</li>

<li><a href="percolation/index.html"><b>Percolation</b></a>. The nature of
the geometrical phase
transition for site percolation on a square lattice is illustrated.</li>

<li><a href="qmc/index.html"><b>Quantum Monte Carlo</b></a>. A Monte Carlo simulation of an ideal quantum gas in one, two, or three dimensions.</li>

<li><a href="diffusion/index.html"><b>Diffusion in a solid</b></a>. A
simple Monte Carlo simulation of
particles on a lattice with a maximum of one particle per site.</li>

</ol>

<p>The Open Source Physics Java code library is described in Wolfgang
Christian, <i>Open Source Physics: A User's Guide with Examples</i>,
&copy; Addison-Wesley, 2007.</p>

<p class="small">Updated 13 May 2008.</p>

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